Practice Complex Powers And Roots (5.12) - Complex Exponential Function

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9 questions

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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the expression for z^2 if z = 3e^(iπ/6)?
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Remember to square the modulus.
Question 2.
Find the modulus of the complex number z = 1 + i.
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Use Pythagorean theorem!
3Question 3.
What is the formula for complex power?
- z^n = r^n e^(inθ)
- z^n = r^n e^(θ)
- z^n = re^(nθ)
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Consider how the power affects both magnitude and direction.
4Question 4.
True or False: The nth roots of a complex number are always positioned randomly.
- True
- False
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Think about symmetry in their distribution.
Question 5.
Find all sixth roots of the complex number z = 64e^(iπ).
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Remember to divide the angle by 6 and account for the full rotation with 2π.
Question 6.
Solve for z^n = (1 + i) where n = 3 using exponentials.
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Expressing initially in polar form simplifies the process.

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